Question: Simplify; express your answer in exponential form. Assume $z\neq 0, t\neq 0$. $\dfrac{{(z^{-5})^{-1}}}{{(z^{4}t^{-5})^{-4}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${z^{-5}}$ to the exponent ${-1}$ . Now ${-5 \times -1 = 5}$ , so ${(z^{-5})^{-1} = z^{5}}$ In the denominator, we can use the distributive property of exponents. ${(z^{4}t^{-5})^{-4} = (z^{4})^{-4}(t^{-5})^{-4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(z^{-5})^{-1}}}{{(z^{4}t^{-5})^{-4}}} = \dfrac{{z^{5}}}{{z^{-16}t^{20}}}$ Break up the equation by variable and simplify. $\dfrac{{z^{5}}}{{z^{-16}t^{20}}} = \dfrac{{z^{5}}}{{z^{-16}}} \cdot \dfrac{{1}}{{t^{20}}} = z^{{5} - {(-16)}} \cdot t^{- {20}} = z^{21}t^{-20}$.